Diabollokus wrote:That polyhedral is very impressive, did you design it yourself or make it from another inspirational source? totally beyond any paper thing I could do.
It's a
well-known mathematical entity discovered/invented a few hundred years ago by either Kepler or Laplace, I think. I first encountered the thing in a book at a library maybe 8 years ago. So no, no freaking way I designed the thing, I just saw some pictures and wanted to make one.
I used to have a nifty VRML animation showing how this and a couple other stellations relate to the usual convex icosahedron. In short, the 12 outer points are the vertices -- the rest of the intersections are face crossings, so they don't count -- and there are 20 big equilateral triangles stretching between those vertices. There are 50-something other similar configurations that come from the icosahedron, a few from the dodecahedron, and one from the octahedron. Stellation patterns define the allowable face shapes.
Intuitively, stellation consists of stretching the faces outward until they cross each other, which tends to make star-like patterns (hence the word). First stellations aren't that hard to visualize, but higher ones are.
Though it's in this thread as well!
It just sucks that I have a really poor concept of 3D! 
so it's really a difficult task for me.
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